Piezoelectrics and ferroelectrics (a special family of piezoelectrics) have wide applications, such as sensor, actuators, and memory devices. Switchability and rotatability of polarizations and domains are of the vital importance in ferroelectric and piezoelectric materials, because the major functions of ferroelectrics are realized by the switching/rotating properties. For memory devices, high signals and low threshold voltages are desired. For sensors, high signal and good agility are desired. For actuators, low voltage application, quick response and large deformation is desired. All of these applications of piezoelectric materials perform based on the switchability and rotatability of polarizations and domains.
For example, the key indices of the performance of ferroelectrics are the polarization and the coercive field. The larger the polarization, the larger the signal; the smaller the coercive field is, the easier for the polarization to switch. As the switching and rotation will cause a change in energy, such as electric energy, elastic energy and gradient energy, and incompatibility may exist within the ferroelectrics, and also between the ferroelectrics and the environment, polarizations in all unit cells may have difficulty switching or rotating to align in one direction because of the difficulty in overcoming the energy barriers brought by the incompatibility. Such difficulty may hinder the performance of these materials, especially in polycrystalline materials which have much more incompatibility intergranually and in thin films that may have a fundamental incompatibility problem between the films and the substrates.
In the research area of ferroelectrics, the term of “twin” usually refers to domain twins, which in tetragonal ferroelectrics may also be referred to as (110) twins. These types of twins are generated by the difference in polarization in adjacent areas, and the polarizations may change directions or even disappear below the Curie temperature under external loading (such as mechanical loading and/or electric field loading). For example, in such tetragonal perovskites, if neighboring domains in one grain (or a single crystal) take <100> direction and <010> direction respectively as the polarization direction, the lattices may be elongated along an orthogonal axis, forming an imaging structure with respect to a (110) plane. This structure is typically referred to a (110) domain twin structure. The domain twin structure is believed to relieve the strain energy which rises from mechanical constraints. However, in the domain twin structure, each of the domains forming the twin may have only three strain variants in total, which may limit elongation compatibility between polarizations of adjacent grains or polarizations between the material and the substrate.